In this paper, we first introduce cohomology groups of all orders for Lie-Yamaguti algebra, and using this cohomology we study a one-parameter formal deformation theory. Our main aim of the present paper is to study Lie-Yamaguti algebras equipped with finite group actions. We define group actions on Lie-Yamaguti algebras following Bredon's [1]} idea for the topological \(G\) -spaces. We provide some examples of equivariant Lie-Yamaguti algebras. Next, we define equivariant cohomology for Lie-Yamaguti algebras. We also develop an equivariant formal deformation theory for Lie-Yamaguti algebras equipped with group actions and show that this equivariant deformation is controlled by our equivariant cohomology. We also obtain some classical deformation-related results following Gerstenhaber [2]}, [3]}, [4]}, [5]}, [6]} deformation theory for associative algebras.
